The roots of $|x - 2|^2 + |x - 2| - 6 = 0$ are

If $\alpha, \beta$ are the roots of $x^2 + px + 1 = 0$ and $\gamma, \delta$ are the roots of $x^2 + qx + 1 = 0$,then $q^2 - p^2$ =

If $\frac{1}{\sqrt{\alpha}}$ and $\frac{1}{\sqrt{\beta}}$ are the roots of the equation $ax^2 + bx + 1 = 0$ $(a \neq 0, a, b \in R)$,then the equation $x(x + b^3) + (a^3 - 3abx) = 0$ has roots:

Consider the equation $x^2+x-n = 0$,where $n \in N$ and $n \in [5, 100]$. The total number of different values of $n$ such that the given equation has integral roots is:

If ${x^2} + 2x + 2xy + my - 3$ has two rational factors,then the value of $m$ will be

If $\alpha$ and $\beta$ are the roots of the equation $2x^{2} - 3x + 1 = 0$,form an equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.